living out of my prius c

The other forum I frequent is ExpeditionPortal, where portable fridges are very common items in vehicles. I've never gone that route myself (I use a cooler and ice) but some things I have picked up from over there:

Thermo-electric coolers are quite limited in ability. They are usually only able to maintain a set number of degrees below surrounding temperature, which in some cases, is not very cold, and they are not very energy efficient.

12v compressor fridges (although much more expensive) are what you want if you want to maintain refrigerator-like temperature. They are much more capable and energy efficient, although they still draw a considerable amount (more than you'd want to connect to a starting battery). It can be difficult to determine the exact amount they use (in terms of Amp-hours), since they cycle variably.

The usual way to power a 12v fridge is to use a second battery (of deep-cycle or gel-cell type) which is usually recharged either with a solar panel (usually 50+ watts) and charge controller and/or a relay/isolator connected to the vehicle's 12v system.

Here is ExPo's review of several 12v compressor fridges, although probably larger than you have in mind:
Overland Journal Portable 12V Fridge Review | Expedition Portal

Kudos on the nomadic lifestyle. That's something many (myself included) lack the courage to do.